Lesson summary
3.1.3 Linear Momentum — AS PHYSICS 9702 notes: Define linear momentum, use p = mv with signs, and find changes of momentum.Linear momentum p = the product of mass and velocity: p = mv.Unit — kg m s-1, equivalent to N s.Momentum is a vector — in the same direction as the velocity.…
- A large mass or a large speed, or both, gives a large momentum
- In one dimension choose a positive direction
- Two equal trolleys moving at equal speeds in opposite directions
- In two dimensions
- A ball that bounces back from a wall at the same speed
- The total momentum of a system
Section 1 of 10Definition
Definition
Linear momentum p
Linear momentum p the product of mass and velocity: p = mv.
Unit
- Unit kg m s-1, equivalent to N s.
Momentum is a vector
- Momentum is a vector in the same direction as the velocity.
A large mass or a large speed, or both, gives a large momentum
- A large mass or a large speed, or both, gives a large momentum it measures how hard a moving object is to stop.
Convert grams to kg and km s-1 to m s-1 before calculating.
Section 2 of 10Direction and signs
1In one dimension choose a positive direction
- In one dimension choose a positive direction objects moving the other way have negative momentum.
2Two equal trolleys moving at equal speeds in opposite directions
- Two equal trolleys moving at equal speeds in opposite directions have total momentum zero.
3In two dimensions
- In two dimensions resolve momentum into components and treat each separately.
4A ball that bounces back from a wall at the same speed
- A ball that bounces back from a wall at the same speed has momentum of the same magnitude but reversed, so it changes by 2mv.
Section 3 of 10Systems of objects
Systems of objects
The total momentum of a system
The total momentum of a system the vector sum of the momenta of its parts, ptotal = mAvA + mBvB.
If two bodies join and move together
- If two bodies join and move together use the combined mass with their common velocity, p = (mA + mB)v.
This is the basis of the conservation of momentum (see 3.3).
Section 4 of 10Change in momentum
1Δp
Δp pfinal − pinitial = mv − mu
- for an object of constant mass.
2This is a vector subtraction
- This is a vector subtraction take care with signs for a rebound.
3A change in momentum needs a resultant force acting for a time
- A change in momentum needs a resultant force acting for a time force is the rate of change of momentum.
4The area under a force-time graph
- The area under a force-time graph is the change in momentum.
Section 5 of 10Momentum compared with kinetic energy
1Momentum p = mv
- Momentum p = mv a vector, which can be negative or zero for a moving system.
2Kinetic energy Ek
½mv2
- a scalar that is never negative.
3They are related by Ek
They are related by Ek p2 ÷ 2m
- so for a given momentum a lighter object has more kinetic energy.
4Doubling the speed doubles p
- Doubling the speed doubles p but quadruples Ek.
Section 6 of 10Why momentum matters
1Crumple zones and airbags
- Crumple zones and airbags lengthen the time over which a passenger's momentum is reduced, so the average force is smaller.
2Recoil
- Recoil a rifle and bullet have equal and opposite momenta, so the heavy rifle gets a much smaller velocity.
3Rocket propulsion
- Rocket propulsion the exhaust gas gains momentum backward and the rocket gains an equal momentum forward.
4Gas pressure
- Gas pressure arises from the momentum change of a very large number of molecules hitting a wall.
Section 7 of 10Typical momenta
| Object | Approximate momentum |
|---|---|
| Walking person, 70 kg at 1.5 m s-1 | about 100 kg m s-1 |
| Car on a road | about 2 × 104 kg m s-1 |
| Air molecule, 5 × 10-26 kg at 500 m s-1 | about 2.5 × 10-23 kg m s-1 |
Section 8 of 10More from the specification
More from the specification
Linear Momentum Definition and Units
- Linear momentum is defined as the product of an object's mass and its velocity (p = mv), having SI units of kg m s-1 or N s,
- and is a vector quantity pointing in the direction of motion.
Newton's Second Law and Net Force
- Newton's second law of motion states that the resultant force exerted on a body is directly proportional to the rate of change of momentum;
- (F = Delta p / Delta t)
- when mass is constant, this yields the fundamental equation F = ma.
Mass and Gravitational Weight
- Mass is the intrinsic quantity of matter in an object resisting acceleration,
- whereas weight is the downward gravitational force exerted on that mass by a gravitational field, calculated from W = mg.
Impulse and Impact Forces
- When colliding bodies strike an obstacle, the impulse of the resultant force equals the change in momentum,
- (F * Delta t = Delta p)
- allowing engineers to determine peak deceleration forces.
Vector quantity
- A quantity with both magnitude and direction.
Solar system
- A star with the objects that orbit it.
Newton
- Unit of force, kg m s-2.
Acceleration
- Rate of change of velocity.
Weight
- Gravitational force on a mass.
Balanced
- Having equal and opposite moments.
W = mg
What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg−1 on Earth)
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Linear momentum | The product of mass and velocity, a vector. |
| Change in momentum | Final momentum minus initial momentum. |
| Impulse | Force multiplied by the time it acts, equal to the change in momentum. |
| Vector | A quantity with magnitude and direction. |
| Kinetic energy | Energy of a moving object, ½mv2. |
| Recoil | The backward motion of a gun when it fires. |
| System | The group of objects being considered. |
| Crumple zone | A part of a vehicle that deforms to lengthen the time of a collision. |
Section 10 of 10Exam technique
1
Treating momentum as a scalar and ignoring direction.
2
Confusing momentum with kinetic energy — doubling the speed doubles p but quadruples Ek.
3
Forgetting to reverse the sign of the velocity after a bounce when finding Δp.
4
Writing the unit as kg m s-2 instead of kg m s-1.